List of useful links  ordered by topic

 At this page you find some selected links ordered by topic, where we have laid emphasis on interactive learning material which needs no download or additional software, although some spreadsheets (requiring Microsoft Excel to run on your computer) and other media have been included. For a refined search on this page use your browser's search functionality (Menu Edit ® Find in Page or the key combination Ctrl F)!

 Links ordered by topic Numbers Prime number generator (applet) Generates a list of prime numbers. Prime Number List and a modified version, whose output looks nicer when printed (JavaScript) Also generate lists of prime numbers. Prime Factorization Machine (JavaScript) Decomposes a given number into its prime faktors. (The maximum number admitted depends on your browser: usually a million). The Prime Machine (applets) Generates prime numbers by means of the Sieve of Eratosthenes and illustrates theorems and conjectures about prime numbers. Also see Notes and Literature on Prime Numbers and The 1000 smallest prime numbers. The Prime Pages. What you always wanted to know about prime numbers. Comprehensive collection of information and links. GIMPS finds 2^3021377-1 is prime. The largest known prime, found in January 1998 (Status of July 1998). The Pi Page and The Uselessless of Pi and its irrational friends offer information and links concerning the number p as well as other number theoretic issues. Also see The p Pages. You can look at the first hundred thousand decimal digits of p. Also see Archimedes and the Computation of Pi (applet). Table of Mathematical Constants. A long list, of course containing p und e, ordered by size, with additional links. Alternatively: ordered by mathematical topic. Inverse Symbolic Calculator is a collection of programs and tables about mathematical constants. Vernier (applet) Very nice illustration of the Nonius principle. Resources on number theory of the Math Forum. Here you find numerous offers on the topic. Bachelor of Arts in Math: Math Resources provides a list of activities and lessons, glossaries, college math courses and journals. Elementary geometry Pythagorean Theorem (applet) Two versions of the proof, realized in a marvellous way. The steps of the proof can be done by the user him/herself The Theorem of Pythagoras (applet) The proof in a version where the user just watches. The Theorem of Pythagoras (applet) Nice interactive diagram illustrating the proof. Pythagorean Theorem (animated graphics) The proof in a version where the user just watches. Pythagorean Theorem. 29 proofs of the theorem and further links. The Euler Line of a Triangle (applet) Euclid's Elements in a web version, with built-in applets which serve for illustration. TheKnotPlot Site offers material and visualization on mathematical knots. Platonic bodies (applet) Rotating wire models of tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron. 3d visualizer of mathematical figures (applet) From the tetrahedron and the Möbius strip to the teapot. Linear algebra Graphing Linear Equations (applet) Learning program on linear functions and their graphical representation as straight lines in a plane. Includes tutorial, test, quiz, crossword puzzle and - as tools - the possibility to plot graphs of functions and a calculator. You may pose questions to the teachers and discuss with pupils of the Bremen High School, USA. Graph Applet (applet) A straight line may interactively be moved, the coefficients m and b of its equation are shown. Java Script Linear Algebra (JavaScript) Some pages about how to manipulate 3 × 3 matrices (multiply, invert,...) and systems of linear equations in 3 variables. A particularly useful tool is the Java Script Linear Algebra Calculator. On page III systems of equations may be solved numerically. The same author also offers a Matrix Calculator Applet capable of dealing with n × n matrices, and a short outline of the mathematics behind (also see his maths pages). Linear Equation Solver (applet) Numerical Solution of systems of linear equations in 3 variables. HartMath (applet) Symbolic manipulation with vectors and matrices in a Java based online computer algebra system. Vectors Vector Arithmetic (some applets) Elementary operations with vectors, e.g. a nice 3D visualization of the significance of vector components. The Vector Cross Product (applet) 3D visualization Trigonometric functions and trigonometry Trigonometry (some applets) A number of units to illustrate definitions, graphs and simple properties of the trigonometric functions, including the Sum Formulae, the Law of Sines and the Law of Cosines. In particular see two applets about the graphs of the Sine and the Cosine function and a further applet by which the definitions of the various trigonometric functions may be compared. Curves Famous Curves (graphics and applets) More than sixty famous plane curves or families of curves are discussed and represented graphically. In the applet versions their parameters may be changed interactively. See also the Famous Curves Applet Index. (School of Mathematical and Computational Sciences, University of St Andrews, Scotland). A Visual Dictionary of Special Plane Curves: A lot of information on curves and families of curves. Resources in various formats: images, Mathematica notebooks, Quick Time movies, Sketchpad and Cabri files. Integration Integration Applet (applet) After typing in a function, the definite Integral is represented graphically as area and its value is shown. Probability and statistics StatApplet (applet) A simple statistics program and a short outline of the mathematics behind. WebStat (Applet) Statistics package, offering numerical and graphical standard methods. Virtual Laboratories in Probability and Statistics (Text, Applets) Extensive online tutorial on probability and statistics. Collelation Visualized (spreadsheet) See a data set with a given correlation coefficient, and change the correlation by moving a slider. Financing Retirement Payments in the Future in Austria: Some Scenarios (spreadsheet) Demographical models for Austria, USA, and Japan (spreadsheet) VassarStats Web Site for Statistical Computation (several JavaScripts) Online programs on topics like statistical tests, simulation, correlation and regression. However be cautious: Feeding them with numerical values in forbidden ranges may cause a browser crash! Numerical methods Bisection Method Tutorial (applet) Illustates the bisection method to numerically solve equations of the form f(x)=0 for some selected functions f. Numerical Integration Tutorial (applet) Some methods for numerical integration are applied to a number of selected functions and illustrated graphically in a nice way. Fractals Mandelbrot Explorer. Stepwise zoom into the mandelbrot set! (Easy to handle: choose a zoom factor and click at an arbitrary point). Julia and Mandelbrot Set Explorer. Zoom program. The author's Pix Gallery provides further material and visualizations on fractal and chaos issues. The Mandelbrot Set (applet) Very nice Mandelbrot images. The loading times are long, but it is worth waiting. Fractals in Science (some applets) A number of visualizations on fractals, random walk and applications in molecular dynamics, provided by the Center for Polymer Studies (Boston University). Image gallery and fractal related software on download. Particularly helpful for beginners: Fractal Coastlines and the Monte Carlo Estimation of Pi. The Fractal Microscope provides some web pages with images and diverse information about fractals and their visualization on modern supercomputers. Fractal pictures and animations. Archive of images and (downloadable) videos on fractals. Mandelbrot Exhibition. Links to websites on fractals and chaos. Sprott's Gateway. Unter the heading "Fractals" you find some links leading to material about fractals. In particular see Carlson's Fractal Gallery. Mandelbrot Set Programs And Links. Review of fractal related software, partially on download. The School of the Web by M. Casco provides rich material and online animations on chaos theory and fractals. Ulli's Fractal Home is a rich site offering material on fractals (interactive applets, graphics, texts and download). Fractal Science Kit. Program package enabling the generation of fractals. Fourier analysis Realtime Fourier sound synthesis (spreadsheet) Sound generator: Determine the intensities of overtones by means of a scroll bar and listen to the according sound. (Even without sound utility, the graphical side of this spreadsheet is a nice illustration of the Fourier series). History of mathematics Math History of the Math Forum Internet Resource Collection. Numerous links. Biographies of Women Mathematicians. Also offers related resources on the web. MacTutor History of Mathematics archive (in particular see the History Topics Index). Earliest Known Uses of Some of the Words of Mathematics and Earliest Uses of Various Mathematical Symbols by Jeff Miller, Gulf High School, USA. And... Cornell University Library Math Book Collection - more than 570 math books were scanned form the originals and may be read online. Unsolved Mathematical Problems. A long list. ...last but not least: Mathematics as a problem Professor Freedman's Math Help. About math anxiety and frustration. www.lernstudio.de. About cognitive math problems and therapies.

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